Saint-Venant’s Principle in Dynamics of Structures

Abstract

Research studies aiming at examination and formulation of a dynamic analog to SaintVenant's principle (DSVP) are critically reviewed. Article concentrates on isotropic homogeneous linear elastic response over a range of structural geometries including waveguides, with either free or constrained lateral surfaces, half space, wedges and cones. Nearly 140 DSVP related references are covered starting with early ideas by Boley. A special chapter is dedicated to available experimental work on end effects and decay rate in dynamically excited structures. Current thinking on possible versions of DSVP is classified into several categories, one of which, the dynamic equivalence, is compatible with much of known experimental data and has been tacitly applied at various engineering situations. That observation provides inspiring ground for renewed interest in both practical and theoretical aspects of DSVP.

Investigation of the 2D assumption in the image‐based inertial impact test

“…As observed in the back‐to‐back imaging experiments (Sections 4.2 and 4.3), the effect on the compressive loading decreases with increasing distance from the impact edge. This is believed to be a result of the Saint‐Venant effect in dynamics, as reported by others, [ 30,31 ] which acts to even out the wave as it propagates away from the impact edge. The reason the three‐dimensional effects amplify as the material unloads is a result of structural dynamics of the sample.…”

Dynamic Localization Phenomena in Elasticity, Acoustics and Electromagnetism

“…Note: This article is an extended and updated version of a review published few years ago in Applied Mechanics Reviews (Karp and Durban, 2011). The theoretical basis of the DSVP should be widened and it is hoped that the present review will contribute towards formulating a unified theory, compatible with the body of knowledge already available, on a dynamic analogue of Saint-Venant's principle.…”

“…It is largely based on a recently published review by Karp and Durban (2011) with several extensions and updates. It is largely based on a recently published review by Karp and Durban (2011) with several extensions and updates.…”

Experimental and numerical study of the interaction between dynamically loaded cracks and pre-existing flaws in edge loaded PMMA specimens

“…Under such loading conditions, the propagating stress wave will have to interact with the pre-existing flaws before reaching the crack tip. Since the characteristic lengths of such specimens are not necessarily sufficiently large for the dynamic version of the Saint-Venant's principle to be invoked [48], the perturbation to the stress wave front, caused by the pre-existing flaw, will not self-correct by the time it reaches the crack tip, and as such may lead to local variation the established mode I field.…”